Calculus Examples

Find the Derivative - d/d@VAR f(x)=((x-4)/(x+2))^3
Step 1
Differentiate using the chain rule, which states that is where and .
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Step 1.1
To apply the Chain Rule, set as .
Step 1.2
Differentiate using the Power Rule which states that is where .
Step 1.3
Replace all occurrences of with .
Step 2
Differentiate using the Quotient Rule which states that is where and .
Step 3
Differentiate.
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Step 3.1
By the Sum Rule, the derivative of with respect to is .
Step 3.2
Differentiate using the Power Rule which states that is where .
Step 3.3
Since is constant with respect to , the derivative of with respect to is .
Step 3.4
Simplify the expression.
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Step 3.4.1
Add and .
Step 3.4.2
Multiply by .
Step 3.5
By the Sum Rule, the derivative of with respect to is .
Step 3.6
Differentiate using the Power Rule which states that is where .
Step 3.7
Since is constant with respect to , the derivative of with respect to is .
Step 3.8
Combine fractions.
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Step 3.8.1
Add and .
Step 3.8.2
Multiply by .
Step 3.8.3
Combine and .
Step 3.8.4
Move to the left of .
Step 4
Simplify.
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Step 4.1
Apply the product rule to .
Step 4.2
Apply the distributive property.
Step 4.3
Apply the distributive property.
Step 4.4
Combine terms.
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Step 4.4.1
Multiply by .
Step 4.4.2
Multiply by .
Step 4.4.3
Multiply by .
Step 4.4.4
Multiply by .
Step 4.4.5
Subtract from .
Step 4.4.6
Add and .
Step 4.4.7
Add and .
Step 4.4.8
Multiply by .
Step 4.4.9
Multiply by by adding the exponents.
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Step 4.4.9.1
Use the power rule to combine exponents.
Step 4.4.9.2
Add and .